Protecting images with an image watermark

ABSTRACT

A robust means of watermarking a digitized image with a highly random sequence of pixel brightness multipliers is presented. The random sequence is formed from ‘robust-watermarking-parameters’ selected and known only by the marker and/or the marking entity. A watermarking plane is generated having an element array with one-to-one element positional correspondence with the pixels of the digitized image being marked. Each element of the watermarking plane is assigned a random value dependent upon a robust random sequence and a specified brightness modulation strength. The so generated watermarking plane is imparted onto the digitized image by multiplying the brightness value or values of each pixel by its corresponding element value in the watermarking plane. The resulting modified brightness values impart the random and relatively invisible watermark onto the digitized image. Brightness modulation is the essence of watermark imparting. Detection of an imparted watermark requires knowing the watermarking plane with which the watermark was imparted. Regeneration of the watermarking plane requires knowledge of the robust-marking-parameters used in its formulation. This is generally only known to the marker and/or marking entity. Once regenerated, the watermarking plane is used together with a verifying image located in a ‘visualizer’ to demonstrate the existence of the watermark. The process of watermark detection is enhanced by application of a blurring filter to the marked image before detection is attempted.

This application is a continuation-in-part of application Ser. No.09/098,233, filed Jun. 16, 1998, now U.S. Pat. No. 6,577,744, which is adivision of application Ser. No. 08/738,930, filed Oct. 28, 1996, nowU.S. Pat. No. 5,825,892.

FIELD OF THE INVENTION

This application relates to the field of digital imaging. It is morespecifically concerned with the insertion and detection of anidentifying mark on a work-piece.

BACKGROUND OF THE INVENTION

It is a constant endeavor to find improved techniques of placing avisible or invisible identifying mark on an image. This is generallyuseful to establish ownership, origin and authenticity, and also todiscourage those who might wish to purloin or misappropriate the work.Identifying marks are also useful to give evidence of unauthorizedalteration or disclosure. Visible marks are herein classified as beingeither visible robust or visible fragile. A mark is classified asvisible robust if it can be seen by the unaided eye and cannot be easilyremoved from the work-piece, if at all, without leaving telltaleevidence. It is classified as visible fragile if the mark itself isvisibly altered by an attempt to alter the work-piece or its wrapper.

Invisible marks are herein classified relative to the appearance of thatmark to a human being with normal visual acuity. A mark on an image isclassified as having an invisibility classification level ofundetectably invisible if, when the image without the marking isdisplayed together with an image copy with the marking, the human beingis equally likely to select either of these copies. An undetectablyinvisible mark is below or at the human being's just noticeabledifference. A mark on an image is classified as having an invisibilityclassification level of subliminally invisible if the mark is notdistracting to the human viewer, although it is above the human being'sjust noticeable difference. An image mark is classified as beingmarginally invisible if it does not cause the marked image to lose itsusefulness or value because of the mark. An image marking is classifiedas being poorly invisible if the marking causes a reduction in theusefulness and/or value of the image.

Presently, both visible and invisible markings of hardcopy documents areused as a generally dependable method of establishing ownership andauthenticity. These time-tested methods are also useful for marking a“softcopy” digitized image, also referred to herein as an image. Adigitized image is an abstraction of a physical image that has beenscanned and stored in a computer's memory as rectangular arrays ofnumbers corresponding to that image's (one or more) color planes. Eacharray element corresponding to a very small area of the physical imageis called a picture element, or pixel. The numeric value associated witheach pixel for a monochrome image represents the magnitude of itsaverage brightness on its single color (black and white) plane. For acolor image, each pixel has values associated and representing themagnitude or average brightness of its tristimulus color componentsrepresenting its three color planes. Other image representations havemore than three color components for each pixel. A different componentvalue is associated with each different one of the image's color planes.

In what follows, whenever reference is made to color planes it isunderstood to include any number of color planes used by a particularimage's digitizing technique to define the pixel's colorcharacteristics. This includes the case when there is only a singleplane defining a monochrome image.

A digitized image is recognizable as an image to a human viewer onlywhen the individual pixels are displayed as dots of white or coloredlight on a display or as dots of black or colored inks or dyes on ahardcopy. Pixels are normally spaced so closely as to be unresolvable bythe human visual system. This results in the fusion of neighboringpixels by the human visual system into a representation of the originalphysical image. Image fusion by the human visual system makes invisiblemarking, or relatively invisible marking, of images possible. Thisproperty is fully exploited by the methods described here to both impartupon a digitized image an invisible watermark to a desired invisibilityclassification, and to subsequently demonstrate its existence. Theimparting and demonstrated detection of a robust invisible marking ondigitized images, herein called invisible watermarking, are a primaryaspect of the present invention.

Properties of a Robust Invisible Watermark

A proper invisible watermarking technique that imparts an invisiblewatermark upon a proprietary digitized image should satisfy severalproperties. The imparted watermark should appear to be invisible to anyperson having normal or corrected visual accommodation to a desiredinvisibility classification level. Clearly, the degree of marking is adichotomy. A balance has to be struck between protecting the image fromunauthorized uses and not having the watermark unpleasantly alter theappearance of the image. This generally means that a recognizablepattern should not appear in the marked image when the watermark isapplied to a uniform color plane. This requirement discourages markingthe image by varying the hue of its pixels, since the human visualsystem is significantly more sensitive to alterations in hue than inbrightness. The requirement can be satisfied by a technique based onvarying pixel brightness implemented in a proper way. A technique basedon varying pixel brightness also allows the same marking techniqueapplied to color images to be equally applicable to monochrome images.

Another property of a proper invisible watermarking technique is that itshould have a detection scheme such that the probability of afalse-positive detection is vanishingly small. For purposes of thepresent invention, the probability of detection of a watermark in animage when one does not exist should be less than one in a million.There is generally little difficulty satisfying this requirement whenthe technique is statistically based.

Still another property of a proper watermarking technique is that itshould be possible to vary the degree of marking applied to an image. Inthis way, the watermark can be made as detectable as necessary by theparticular application. This property is important in highly texturedimages where it is often necessary to increase the intensity of the markto increase its likelihood of detection. This is in contradistinctionwith images that have low contrast in which it is advantageous to reducethe marking intensity to lessen undesirable visible artifacts of thewatermark itself.

It is also highly desirable that when detected the demonstratedexistence of the watermark should be translatable to a recognizablevisual image having relatively bold features with a high contrast ratio.Features of a demonstrated visual image that are not relatively bold mayotherwise be difficult to show if the watermark has been attacked inattempts to defeat its protection.

Finally, the imparted watermark should be robust in that it should bevery difficult to be removed or rendered undetectable. It should survivesuch image manipulations that in themselves do not damage the imagebeyond usability. This includes, but is not limited to, JPEG “lossy”compression, image rotation, linear or nonlinear resizing, brightening,sharpening, “despeckling,” pixel editing, and the superposition of acorrelated or uncorrelated noise field upon the image. Attempts todefeat or remove the watermark should be generally more laborious andcostly than purchasing rights to use the image. If the image is of rarevalue, it is desirable that the watermark be so difficult to remove thattelltale traces of it can almost always be recovered.

SUMMARY OF THE INVENTION

An aspect of the present invention is to provide a method for impartinga watermark onto a digitized image comprising the steps of providing thedigitized image, and multiplying the brightness data associated with atleast one of the image pixels by a predetermined brightness multiplyingfactor. The image includes a plurality of pixels, wherein each of thepixels includes brightness data that represents one brightness value ifthe image is monochrome, or a plurality of brightness data values if theimage has multiple colors. A brightness data value of a pixel and acolor component or component are hereinafter used to mean the samething, and are therefore to be considered interchangeable. In anembodiment, the brightness multiplying factor ranges from 0.5 to 1.0.Other smaller or larger factors are useful in some image applicationsdependent upon particular desired watermarking results. The brightnessmultiplying factor has a relationship with a number taken from a randomnumber sequence and the relationship is a linear remapping to provide adesired modulation strength.

In an embodiment, each of the pixels has a row and a column location inan array representing the digitized image, and the brightnessmultiplying factor employs a different sequential combination of numbersfrom a robust random number sequence in sequential correspondence to therow and column location.

Another aspect of the present invention is to provide a method forgenerating a watermarked image wherein a watermark is imparted onto adigitized image having a plurality of original pixels, each pixel havingoriginal brightness values. The method includes the step of providing adigitized watermarking plane comprising a plurality of watermarkingelements, each having a brightness multiplying factor and havingone-to-one positional correspondence with the original pixels. It alsoincludes the step of producing a watermarked image by multiplying theoriginal brightness values of each of the original pixels by thebrightness multiplying factor of a corresponding one of the watermarkingelements wherein the watermark is invisible. In an embodiment, when theoriginal image forms an original plane and the watermarking plane issmaller than the original plane, the method further includes the step ofextending the watermarking plane by tiling such that the watermarkingplane covers the original plane and/or further comprises the step oftruncating the watermarking plane such that the watermarking planecovers the original plane, upon determining that the watermarking planeextends beyond the original plane.

Another aspect of the present invention is to provide a method forforming a watermarking plane including a plurality of elements eachhaving a multiplying value. The method comprises the steps of:generating a robust random sequence of integers having a first pluralityof bits; linearly remapping the random sequence to form a remappedsequence of brightness multiplying factors to provide a desiredmodulation strength; computing a discrete Fourier transform of theremapped sequence to form a Fourier sequence having frequencycoordinates; expanding the frequency coordinates to form an expandedsequence; and computing an inverse Fourier transform of the expandedsequence to obtain a watermarking sequence of values.

An embodiment further includes one or more or the following: the step ofexpanding is accomplished by zero-padding; the method further comprisesa step of employing the watermarking sequence to provide the multiplyingvalue for each of the elements; the method further comprises the stepsof hard clipping the watermarking sequence to form a hard-clippedsequence having sequence members, and utilizing a different one of thesequence members to provide the multiplying value for each of theelements; the method further comprises the steps of adjusting thewatermarking sequence to form a normalized sequence of values having amean and a median equal to the difference between unity and themodulation strength, and having a maximum of unity, and employing thenormalized sequence to provide the multiplying value for each of theelements; the method further comprises the steps of providing anunmarked original image having a plurality of original pixels, each ofthe pixels having at least one component, wherein a first number of theoriginal pixels is greater than a second number of the plurality ofelements, expanding the watermarking plane by tiling to cover theunmarked original image such that one of each of the pixels has onecorresponding element from the elements; and multiplying the at leastone component of each of the pixels by the multiplying value of thecorresponding element.

Still another aspect of the present invention is to provide a method fordetecting a watermark in a marked image. The marked image is marked by awatermarking plane which has a plurality of watermarking elements. Eachof the image pixels has at least one component and each of thewatermarking elements has a brightness multiplying factor. The methodemploys a selector having at least one element and a visualizer havingat least one pixel and at least one counter, said at least one counterto store the comparison data resulting from comparisons for each of aplurality of selector elements and positions; said comparison dataresulting from the comparison of the statistical brightness of eachimage color component, relative to its neighboring color components inthe same plane, with the statistical magnitude of each correspondingbrightness multiplying factor, relative to its neighboring multiplyingfactors. The method further comprises the step of displaying avisualizer-coincidence image such that a user can make a determinationas to whether the pattern encoded by the visualizer pixels isrecognizable and thereby, whether the watermark is detected.

Further, it is an aspect of the present invention to provide analternative method and apparatus for imparting a watermark into adigitized image that includes the step of providing the digitized imageand the step of adding at least one predetermined brightness adjustingvalue to the brightness data associated with at least one of the imagepixels. The image includes a plurality of pixels, wherein each of thepixels includes brightness data that represents one component if theimage is monochrome, or a plurality of components if the image hasmultiple colors. The step of “adding a predetermined brightness datavalue to a component” is used in the same way as the step of“multiplying a component by a predetermined brightness multiplyingfactor”, where the component is associated with at least one of theimage pixels. Under conditions that will be specified, the step ofadding achieves image watermarking results which are similar in everymanner and respect to the step of multiplying. The additive brightnessadjusting values may be positive or negative, and a color componentaltered by the step of adding increase or decrease accordingly.

In another aspect of a general embodiment, the components of all imagepixels, or all image pixels in a specified image portion, are eachmodified by an associated brightness adjusting factor.

In another particular embodiment, each of the pixels has a row and acolumn location in an array representing the digitized image, and thebrightness adjusting factors for each pixel employ a differentsequential combination of numbers from a different robust random numbersequence in sequential correspondence to the row and column location.

Another aspect of the present invention is to provide a method forgenerating a watermarked image wherein watermarks are imparted into adigitized image by having a plurality of original watermarking elements,with each of the elements having an original brightness adjusting value.

Another aspect of the present invention is to provide a method forforming watermarking planes. Each watermarking plane includes aplurality of elements with at least one brightness adjusting valuederived from each element.

Still another aspect of the present invention is to provide a method forimproving the probability of detection of a watermark in a marked imageor a derived copy of a marked image. The marked image is marked by awatermarking plane which has a plurality of watermarking elements. Themethod applies a two-dimensional blurring filter to the marked image orderived copy of a marked image prior to attempted detection of theimparted watermark.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other objects, features, and advantages of the presentinvention will become apparent upon further consideration of thefollowing detailed description of the invention when read in conjunctionwith the drawing figures, in which:

FIG. 1 shows a block diagram of an image capture and distribution systemsuitable for use in accordance with an embodiment of the presentinvention.

FIG. 2 shows an embodiment for forming a watermarking plane inaccordance with the present invention.

FIG. 3 shows an embodiment for the steps of watermark imparting.

FIG. 4 shows an overview of the steps for image alignment.

FIG. 5 shows the steps for a coarse alignment of a marked image with acorrelation reference plane.

FIG. 6 shows the steps for a fine alignment of a marked image with acorrelation reference plane.

FIG. 7 shows the steps for finding a watermark in a marked image.

FIG. 8 shows a random positioning of the selector array over thewatermarking plane and the image planes.

FIG. 9 shows a typical visualizer pattern.

FIG. 10 shows a method of verification of the presence of the watermark.

FIG. 11 shows a detection resulting from the visualizer of FIG. 9 for awatermarking made at a modulation strength of 1%.

FIG. 12 shows a detection resulting from the visualizer of FIG. 9 for awatermarking made at a modulation strength of 2%.

FIG. 13 shows a detection resulting from the visualizer of FIG. 9 for awatermarking made at a modulation strength of 4%.

FIG. 14 shows a detection resulting when the image has no watermark.

FIG. 15 shows the steps for an alternate method of finding a watermarkin a marked image.

FIG. 16 shows an enlarged segment of a watermarked image, having beenwatermarked at a modulation strength of 2.5%, that is used as thereference image.

FIG. 17 shows the enlarged segment of the reference image after it hasbeen prepared for printing by screening, has been printed and has beenscanned to form the derivative image.

FIG. 18 shows the enlarged segment of the derivative image that has beenacted upon by a blurring filter to form the filtered image.

FIG. 19 shows a visualizer-coincidence image resulting from a watermarkdetection made on the reference image.

FIG. 20 shows a visualizer-coincidence image resulting from a watermarkdetection made on the derivative image.

FIG. 21 shows a visualizer-coincidence image resulting from a watermarkdetection made on the filtered image.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides a robust means of watermarking adigitized image with a highly random sequence of pixel brightnessmultipliers. The random sequence is formed from four‘robust-watermarking-parameters’ selected and known only by the markerand/or the marking entity. A watermarking plane is generated which hasan element array with one-to-one element correspondence to the colorcomponent array or arrays of the digitized image being marked. Eachelement of the watermarking plane is assigned a random value dependentupon a robust random sequence and a specified brightness modulationstrength. The so generated watermarking plane is imparted onto thedigitized image by multiplying the brightness value or values of eachpixel by its corresponding element value in the watermarking plane. Theresulting modified brightness values impart the random and relativelyinvisible watermark onto the digitized image. Detection of an impartedwatermark requires knowing the watermarking plane with which thewatermark was imparted. Regeneration of the watermarking plane requiresknowledge of the robust-marking-parameters used in its formulation. Thisis generally only known to the marker and/or marking entity. Onceregenerated the watermarking plane is used together with a verifyingimage located in a ‘visualizer’ to demonstrate the existence of thewatermark.

Brightness modulation is the essence of watermark imparting according tothe present invention. Pixel brightness, as used herein, expresses thebrightness of a visual stimulus in terms of the CIE 1931 StandardColorimetric Observer and Coordinate System tristimulus componentbrightness X, Y and Z that correspond to a matching mixture of threereference stimuli. If the image is monochrome, pixel brightnessexpresses the brightness of a visual stimulus in terms of the CIE 1931Standard Coordinate System photopic brightness Y, and components X and Zhave no meaning. A more detailed description of pixel brightness isfound in G. Wyszecki and W. S. Styles, “Color Science: Concepts andMethods, Quantitative Data and Formulae,” John Wiley & Sons, Inc. (2nded.), New York, 1982, pp. 164–169, incorporated herein by reference inits entirety. The CIE 1931 standard specifies three particular referencestimuli. The stimuli are radiometric quantities, and as such areexpressed in radiometric units such as watts. Grassmann's law, on whichnearly all of modern colorimetry is based, requires use of the threespecific reference stimuli, or three others that are distinct linearcombinations of them. This is discussed in D. B. Judd and G. Wyszecki,“Color in Business, Science, and Industry,” (3rd ed.), John Wiley &Sons, Inc., New York, 1975, pp. 45–47, incorporated herein by referencein its entirety. By modifying only a pixel's brightness, its color,represented by its hue and saturation, is not changed. This isaccomplished by preserving the ratios of X:Y and Z:Y while changing themagnitude of Y. A pixel represented in any nonlinear color space, suchas the color space of the subtractive dyes Cyan, Magenta, Yellow andBlack (CMYK) used in color printing, will be translated to the X, Y, Zcolor space (or to a color space linearly related to it) before thepixel's brightness is modified.

FIG. 1 shows a block diagram of a system embodiment for imparting arelatively invisible watermark on a digitized image in accordance withthe present invention. FIG. 1 shows an image capture and distributionsystem 150 suitable for use in accordance with an embodiment of thepresent invention. A scanner 100 captures image data 101 from a physicalsource 102. The physical source 102 is typically a painting orphotograph. The image sends data 101 to a digital computer 104. Thecomputer 104 includes a working storage 106 that is typically embodiedin the computer's random access memory, an image storage system 108 thatis often a conventional hard disk drive, and an image archive 110 thatcan be a tape or disk storage. The computer 104 also includes a numberof software modules. These include front end image processing software112 that performs image processing such as scaling and enhancement ofthe image data provided by the scanner 100. It also includes colorpreserving watermarking software 114 operating in accordance with theprinciples of the present invention, and back-end image processingsoftware 116 that performs other processing functions such ascompression on the watermarked image. Most often, the unprocessed orfront-end digitized original image 101 is sent to the image archive 110for preservation in unwatermarked form.

An alternate embodiment has the original image already available indigitized form 101 without requiring a scanner 100. The watermarkingsoftware 114 applies a relatively invisible watermark to the digitizedimage 101 in accordance with the principles of the present invention.The watermarking process can also be performed on a copy of an archivedimage or on other scanned and processed image data, which has beenloaded in whole or in part, into the computer's working storage 106.

The processed, watermarked and compressed image produced by thecombination of the software modules 112–116 is sent from the workingstorage 106 or image storage 108 to an image server 118 that isconnected to a digital network 120. When appropriate, the digitalnetwork is interconnected with a Local Area Network (LAN), a Wide AreaNetwork (WAN) such as the Internet, or both. Other systems 122 connectedto the digital network 120 can request and receive images stored on theimage server 118 via the digital network 120. In some cases, the systemscan then display the received images on a display device 124 and/orprint the images on a graphics capable printer 126. Those skilled in theart will recognize that there are many other system configurations inwhich the present invention could be employed. The system of FIG. 1 isgenerally also useful for detecting and demonstrating the existence ofthe watermark in a manner such as those described subsequently.

Marking an Image with a Robust Watermark

In one embodiment, the watermark imparted onto the digitized image is amonochrome pattern, herein called “the watermarking plane,” thatoverlays the digitized image. The pattern is embodied by selecting itselement values from a robust random sequence formed from a group ofrobust sequence generating parameters. The parameters are used togenerate a generally strongly encrypted random sequence in a manner wellknown to those skilled in the art. These parameters are herein referredto as the ‘robust-watermarking-parameters’. In a preferred embodiment,these parameters include a cryptographic key, two coefficients of alinear random number generator, and an initial value of the randomnumber generator.

Each value, or group of values, of the robust random sequence isassociated with one of the pixels of the digitized image. Most often thevalues of the random sequence are linearly remapped to meet particularcriteria. All the brightness values of the plurality of color planes ofeach pixel are multiplied by its associated linearly remapped robustrandom sequence value called its brightness multiplying factor ormultiplying factor. A brightness multiplying factor which modifies pixelbrightness values by less than ten percent is herein referred to as abrightness multiplying factor producing a relatively invisiblewatermark. It is noted that depending on the texture of the image beingwatermarked, the brightness values are generally modified on average bya percentage factor of only 0.3 to 4 percent, and rarely up to 10percent. This is in order to make the marking less visible. Thepercentage factor is herein referred to as the modulation strength. Theactual modulation strength employed is dependent upon the classificationlevel of invisibility required by the particular use. It is notadvisable to employ a brightness multiplying factor greater than unity.This can result in some pixel brightness values being greater than one.If employed, it is recommended that all brightness values greater thanone be clipped to a value of unity. This can alter the pixel's color,thus altering the appearance of the image.

Imparting a watermark upon a digitized image by varying the brightnessof each pixel with a multiplying factor maintains each pixel's color bysatisfying Grassmann's law. A compromise is generally made in selectingmodulation strength. A smaller percentage makes the watermark lessvisible but more difficult to detect. A larger percentage makes iteasier to detect and demonstrate the existence of the watermark, butmakes the watermark more visible. A highly textured image may requirethe use of a relatively high modulation strength. An imparted watermarkis considered to be undetectably invisible in all cases if themodulation strength is less than 0.5 percent, even when the unmarkeddigitized image is a uniform medium gray. For digitized images havingmore practical and valuable features, subliminally invisible watermarksgenerally have modulation strengths of 1% to 3%, depending on the degreeof textural variation in the image itself.

The watermark imparted in accordance with this invention is selected soas to appear to be relatively invisible to any person having normal orcorrected visual accommodation. The probability of a false-positivedetection of the watermark in an image when it does not exist is lessthan one in a million. It is possible to vary the degree of impartedwatermarking onto the image so that the watermark can be made asdetectable as necessary consistent with a required invisibilityclassification. The detected watermark is translatable to a recognizablevisual image, called a visualizer, having relatively bold features andwith a very high contrast ratio. The watermark once imparted, is verydifficult to remove or to be rendered undetectable without reducing theusefulness and/or value of the digitized image.

In an embodiment of this invention, marking a digitized image with aninvisible watermark requires the formation of a plane for watermarking.The invisible watermark is herein represented as a rectangular array ofnumeric elements, henceforth referred to as the watermarking plane,having I rows and J columns. The I rows and J columns correspond to thedimensions of the entire original digitized image, or a portion thereof,to which it is being applied.

When an original digitized image is very large, a generated watermarkingplane not large enough to cover the entire original image is extended bytiling replication in any direction necessary to cover the entire image.If a watermarking plane being so tiled extends beyond any edge of theoriginal image, the watermarking plane is assumed to be truncated. Theseconventions are adopted for this embodiment to allow every pixel of theoriginal image to have its brightness altered and to ensure that themarked image is equal in size to the original image. This forms aone-to-one correspondence between element locations in the watermarkingplane and color components in the color planes of the original image.This is generally a desirable implementation, even though alternateembodiments do not require watermarking the entire image.

In a preferred embodiment, the value of each element in the arraydefining the watermarking plane is linearly remapped to be a randomnumber in the range,1≧w(i, j)≧(1−2β),  (1)where,1≦i≦I,  (2)and1≦j≦J,  (3)are the row and column indices of the array, and β is the modulationstrength of the watermark such that,0.5≧β≧0.  (4)

Additionally, all elements in the generated watermarking plane, treatedas an ensemble, are adjusted to have a mean and median of 1−β.

Imparting the watermark onto an image begins with generation of thiswatermarking plane. The watermark is imparted onto the original image bymultiplying all the brightness values associated with every pixel ineach color plane by the value in its corresponding element in thewatermarking plane.

Constructing the Watermarking Plane

The construction of the watermarking plane is fundamental to insuringthe robustness of the imparted watermark and its ability to survive evendetermined attacks. To this end, the procedure by which the values ofthe watermarking plane elements are chosen is based on cryptographic andtwo-dimensional signal processing theory techniques. These are used tosatisfy particular requisite properties of the watermarking plane.

The Property of Unpredictable Randomness

Consideration is now given to the values of the watermarking planeelements to meet the property of unpredictable randomness. Unpredictablerandomness requires that each element's value should vary randomly fromthe values of its neighbors, and the sequence of element values shouldbe essentially unpredictable. Random variation of the elements isrequired for the watermark to be rendered relatively invisible. In asmuch as pattern recognition is one of the most dominant characteristicsof the human visual system, the presence of any pattern among elementsof the watermarking plane could make it visible. The unpredictability ofthe sequence of values is required to make the watermark robust and lessvulnerable to attack. It is recognized that if all values in thewatermarking plane could be predicted, the watermarking process couldeasily be reversed and the mark removed. This could thereby be used toessentially restore the marked image to a nearly perfect copy of theoriginal unmarked image. Thus, a means of generating a highlyunpredictable random number sequence is preferred.

Generating random values by a congruence method, typical of nearly allpopular pseudo-random number generating algorithms, is not consideredherein to provide an adequate level of unpredictability. These sequenceshave only modest cryptographic strength and are relatively easilydiscernible by crypto-analytic techniques. This is described in “TheCryptographic Security of Truncated Linearly Related Variables,” J.Hastad and A. Shamir, Proceedings of the 17th Annual ACM Symposium onthe Theory of Computing, 1985, pp 356–.362, which is herein incorporatedby reference.

For the purposes of this invention a sequence is generated by using astrong cryptographic method such as the National Standard DataEncryption Algorithm. This is described in: “American National StandardData Encryption Algorithm,” ANSI X3.92-.1981, American NationalStandards Institute, New York; and in A. G. Konheim, et al., “The IPSCryptographic Programs,” IBM System Journal, Vol. 19, No. 2, 1980, pp253–283; which are herein incorporated by reference.

The data sequence of eight-bit values to be encrypted is selected by themarker, and is desirably generated by a congruence algorithm. However,the robust secure sequence is produced by action of the strongencryption algorithm on that data. Using this approach, a highlyunpredictable watermarking plane can be produced. Moreover, it can bereproduced exactly by knowing only its four‘robust-watermarking-parameters’. These parameters are the initial stateand the two coefficients of the congruence algorithm, and thecryptographic key used by the encryption algorithm. These algorithmsgenerally produce sequences of values having eight-bits. Sixteen-bitvalues, referred to as α(i, j), are generated by concatenating two ofthe sequential eight-bit values produced by the encryption algorithm.Each sixteen-bit value so produced is linearly remapped to become anelement of the array defining the watermarking plane as follows:w(i, j)=1−2β[1−α(i, j)/65535]  (5)

Additionally, all elements in the w(i, j) array, treated as an ensemble,are adjusted to have both a mean and median of 1−β. Ease of reproductionof the resulting encrypted sequence is important for watermark detectionand demonstration techniques discussed subsequently. Other remapping ornormalization techniques producing particular desired results are knownto those familiar with the art.

The Property of Explicit Low Frequency Content

Another important consideration is for an embodiment that exploits theproperty of explicit low frequency content. Significant high frequencycontent results when the watermarking plane is composed by placing aunique random value in every element. Although high frequency content isbeneficial in making the watermark less visible, it also makes itvulnerable to attack for watermark damage or extinction. This is evidentfrom the following consideration. The highest pattern frequencyachievable in a digitized image is obtained by replicating a pair ofadjacent pixels that have opposite extreme values. When the image isreduced in size, if image reduction filtering is used, the values ofadjacent pixels are combined in a weighted average to form pixel valuesof the reduced image. If image decimation is used, pixels areselectively discarded. In either event, the high frequency content inthe original image is lost in the reduced image. Any significant highfrequency content in the applied watermarking plane becomes obliteratedin the reduced image. Subsequent detection of the watermark impartedprior to the size reduction is very difficult if not impossible. Thepurposeful addition of low frequency content makes the watermark lessvulnerable to this type of attack. However, the deliberate inclusion ofsignificant low frequency content in the watermarking plane is anotherdichotomy. Its inclusion indeed makes the watermark less vulnerable tonormal image manipulation and therefore more easily detectable. However,it generally makes the watermark more visible by producing a patternwith larger features in the watermarking plane. It is generallypreferable to add only a controlled amount of low frequency content.

The deliberate addition of low frequency content to the originalwatermarking plane is accomplished in one embodiment by employing thetwo-dimensional discrete Fourier transform. First, a reduced-sizewatermarking plane is formed whose elements are uniformly distributedrandom values in accordance with the secure sequence described above.For discussion purposes, a square plane w(μ, ν) having 0≦μ≦Λ−1 rows and0≦ν≦Λ−1 columns is used. The discrete Fourier transform of the squareplane is computed. Since all values of w(μ, ν) are real numbers,advantage can be taken from the complex-conjugate symmetry of itsFourier transform. The complete Fourier transform can be specified asthe array of complex numbers W(σ, τ) having dimensions 0≦σ≦Λ−1 and0≦τ≦Λ/2, and is symbolized as:W(σ, τ)=F[w(σ, τ)]  (6)

The frequency domain array W(σ, τ) is remapped into an expanded arrayW(s, t), where:0≦s≦L−1, 0≦t≦L/2, and L=2^(ρ)Λ,thus enlarging the (σ, τ)-space by the factor 2^(ρ) in each dimensionforming the larger (s, t)-space. If W(σ, τ) is defined such that W(0, 0)is the coefficient of the constant or “zero-frequency” term, then:W(L−s, t)=W(Λ−σ, τ),  (7)andW(s, t)=W(σ, τ),  (8)for0≦s=σ<Λ/2 and 0≦t=t≦Λ/2,  (9)andW(s, t)=0  (10)for all other values of s and t. This technique is herein referred to as“zero-padding.”

The inverse Fourier transform of W(s, t) provides the modifiedwatermarking plane w(m, n) having 0≦m≦L−1 rows and 0≦n≦L−1 columns. If,for example, ρ=2 and Λ=512, then w(m, n) is a square array having 2048rows and columns. More importantly, however, w(m, n) has an assured lowfrequency content with a minimum period (2^(ρ)=2²=4) four times longerthan the minimum period possible in a 2048² image plane. Since itsgenerating kernel, w(μ, ν), contains 262, 144 random values taken from asecure sequence, its vulnerability to attack by brute force replicationis relatively small. In a case where a thus marked image appears to bevulnerable, its kernel can easily be made larger. Still lower frequencycontent can be impressed by using a ρ=3, making the highest frequency tobe one eighth of the original highest frequency. The preferredembodiment uses ρ=2 so as not to over employ low frequency content thatmay cause the watermark to become undesirably visible.

The values of some elements of the generated watermarking plane so farproduced may exceed one. Since each value is to be used as a multiplierof pixel brightness, it is therefore possible to produce a multipliedpixel brightness that is greater than one [i.e. greater than a maximumbrightness], which is a brightness that can not physically be displayed.In this event, any multiplied pixel brightness greater than one wouldhave to be clipped to the maximum that can be displayed. The preferredembodiment, however, employs an additional process step to avoid thepossible need for clipping. Before the generated modified watermarkingplane is used, its elements, forming an ensemble, are adjusted to makeboth their mean and median values equal to 1−β and the maximum valueequal to 1. With these adjustments, the requirement that,1≧w(i, j)≧(1−2β),  (11)for all i and j is satisfied.

At this point, it is sometimes advantageous to “hard clip” the elements.In this situation, elements with values greater than or equal to 1−β areset to 1, and elements with values less than 1−β are set to 1−2β. Hardclipping normally increases the probability of detecting a watermark,but unfortunately, it also tends to make watermarking artifacts morevisible in the marked image.

The Property of Plane Expansion by Tiling

The fact that the watermarking plane w(m, n) is produced as the resultof an inverse discrete Fourier transform is very useful. If thewatermarking plane is not large enough to cover the entire unmarkedimage, if L<I or L<J, it can be enlarged seamlessly by tilingreplication downward or to the right to make a plane as large asdesired, with each tiled extension adding an additional 4,194,304elements. For the example dimensions used here, tiling replication is:w(m′, n′)=w(m, n),  (12)where,m′=(2048p)+m,  (13)n′=(2048q)+n,  (14)and p and q are non negative integers.

In one embodiment, a watermarking plane is formed following the steps202–216 shown in FIG. 2. These steps are herein referred to as the‘ideal interpolator watermarking plane generating method’. Firstly, aneight-bit pseudo-random sequence is generated, 202. The resultingsequence is encrypted to form a secure sequence of eight-bits values,204. Sixteen bit integer samples are formed by concatenating two abuttedvalues from the secure sequence, 206. The sixteen bit integer samplesare linearly remapped and formed into a w(μ, ν) array such that,1≧w(μ, ν)≧(1−2β),  (15)208. The discrete Fourier transform frequency domain array W(σ, τ) iscomputed from w(μ, ν), 210. The W(σ, τ) coordinates are expanded byzero-padding to form expanded frequency domain array W(s, t), 212. Thepreliminary watermarking plane array w(m, n) is computed by taking theinverse discrete Fourier transform of W(s, t), 214. The elements of thepreliminary array w(m, n) are adjusted to collectively have a mean andmedian of (1−β) and a maximum of 1, 216 a. Alternatively, the elementsw(m, n) are hard clipped to have only values of 1 or 1–2β, with a medianof 1−β, 216 b. The resulting adjusted array w(m, n) is the watermarkingplane with elements that are brightness multiplying factors to be usedfor adjusting corresponding pixels of the image being watermarked.

The method presented here, employing forward and inverse discreteFourier transforms to generate the watermarking plane, is an “idealinterpolator” with assured low frequency content. Other methods known tothose skilled in-the-art are available. These include methods that usetwo-dimensional interpolation filters that can similarly be employed toproduce acceptable results.

The generated watermarking plane is then imparted onto the originalunmarked digitized image. FIG. 3 shows an embodiment for the steps ofwatermark imparting. First, the watermarking plane is expanded by tilingto completely cover the image being watermarked, 302. This forms aone-to-one correspondence of an element in the expanded watermarkingplane and a pixel in the original image. The brightness values of eachpixel in the original image are multiplied by the value in itscorresponding element in the expanded watermarking plane, 304. Theresulting image with the new brightness values forms the watermarkedimage. The relative visibility of the watermark in the image is observedin relationship to the desired visibility classification level marking.If the marking is more visible than specified the steps of FIGS. 2 and 3are repeated for a lower modulation strength. A watermark created with alower modulation strength is generally less easily detected anddemonstrated to exist. One the other hand, if the resulting watermark isless visible than specified, the steps of FIGS. 2 and 3 may be repeatedto provide a watermark with a higher modulation strength. A watermarkcreated at a higher modulation strength is generally easier to detectand have its existence demonstrated. Once imparted, an invisiblewatermark only serves its purpose if it can be detected and shown toexist.

Finding an Invisible Watermark Hidden in a Marked Image

It is most desirable to demonstrate the existence of the watermark witha visible image having bold features. This is herein employed using animage array called a “visualizer.” Demonstration of the existence of thewatermark imparted in accordance with the-present invention requires aregeneration of the watermarking plane with which it was marked. Thiscan generally only be performed by the marker and/or marking entity whoalone knows the four parameters making up this application's“robust-watermarking-parameters”′. Knowledge of these parameters isrequired for generating the robust random sequence used in forming thewatermarking plane. From these four parameters the robust randomsequence is reformed. Values of the sequence are used to define thevalues of the elements. If a linear remapping process was employed inthe generation of the watermarking plane, the element values arelinearly remapped using that same process to redefine the expandedwatermarking plane. The thus reformed expanded watermarking plane isused in conjunction with the visualizer to demonstrate the existence ofthe expanded watermarking plane in the image. This is accomplished asdescribed subsequent to an overview of watermark detectionconsiderations.

Finding an invisible watermark hidden in a marked digitized image is arelatively difficult problem, and it is made more so by manipulations ofthe marked image that may have occurred. The watermark survives and isdetectable for image manipulations that in themselves do not damage theimage beyond usability. The detection method of the present inventioncan find an imparted watermark with a high degree of certainty in nearlyall such cases. A significant advantage of the present method is thatwatermark detection does not require access to a copy of the entireoriginal image. In most cases, all that is required is the watermarkingplane used for imparting the watermark on the image. A perfect copy ofthe watermarking plane is reconstituted from its four definingparameters. If a copy or if even only a fragment of the original imageis available, detection can have a somewhat higher probability ofsuccess.

Reorienting and Resizing the Watermarking Plane

A first consideration in finding a watermark is to determine how and byhow much the marked image may have been manipulated. It may have beenreduced in size. A size reduction may even have been performednonlinearly, such that its horizontal and vertical dimensions may havebeen reduced by unequal factors. The image may also have been rotated,not by an obvious ninety degrees, but by a small angle. Facilitatingthis determination is the knowledge that pixel values in theunmanipulated marked image are directly related to correspondingelements in the watermarking plane. If a significant fragment of theoriginal image is available, a fragment of the unmanipulated markedimage can be reconstructed. Either the reconstituted watermarking planeor a reconstructed fragment of the marked image is a suitable“correlation reference plane.”

An overview of the steps of reconstructing a manipulated watermarkedimage is shown in FIG. 4. First, the watermarking plane used forimparting the watermark onto the image is regenerated from the four‘robust-watermarking-parameters’ generally only known to the markerand/or the marking entity, 402. Secondly, the marked image is resizedand rotated to its known original dimensions, 404. Thirdly, the resizedand rotated image is aligned with the expanded regenerated watermarkingplane such as to provide one-to-one correspondence of the elements ofeach with the elements of the other, 406.

In an actual implementation the steps of reorienting and resizing themarked image may be broken into a coarse placement followed by a finealignment. The coarse placement is performed by visual inspection of adisplayed copy of a portion or the complete marked image overlaying acorresponding portion or complete correlation reference plane. Thecorrelation reference plane is reoriented and resized to the size andorientation of the marked image by axis reduction or expansion,translation and/or rotation. This is accomplished using techniques wellknown to those skilled in the art. The coarse placement generally bringsthe correlation reference plane to within 4 percent of the manipulatedmarked image's size and within four degrees of its orientation.

FIG. 5 shows the steps for an embodiment for performing coarseplacement. Both the marked image and the correlation reference plane aredisplayed on a common display, 502. The vertical axis and horizontalaxis magnification, offset and angular rotation of the correlationreference plane display are varied to make the displayed correlationreference plane closely overlay the corresponding portions of thedisplayed manipulated marked image, 504. The values of themagnification/reduction factors, horizontal and vertical offsets andangle of rotation are noted and stored, 506. The entire marked image isrescaled, translated and rotated by the inverses of the noted values sothat it visually matches the correlation reference plane, 508. The socoarsely manipulated reconstituted marked image is further manipulatedto perform the fine alignment.

According to the Fourier Shift Theorem, Rotation Theorem and ScalingTheorem, the properties of translation, rotation and scaling transcendthe Fourier transformation of an image, and, if present in w(m, n), eachwill also be present (or, in the case of scaling, its reciprocal will bepresent) in W(s, t). This is useful to determine a more precise angle ofrotation, horizontal and vertical scale factors, and translation offsetsof the correlation reference plane relative to the marked image. This isaccomplished by first constructing a three-dimensional “array ofphase-correlation maxima.” The three axes of the array correspond to thehorizontal scale factor, the vertical scale factor, and the angle ofrotation of the correlation reference plane relative to the markedimage. Phase-correlation is defined as follows. Let W(s, t) be thediscrete Fourier transform of the correlation reference plane, U(s, t)be the discrete Fourier transform of the marked image u(m, n), and U*(s,t) be the complex conjugate of U(s, t). The phase-correlation plane p(m,n) is computed using the relationship:

$\begin{matrix}{{p( {m,n} )} = {{F^{- 1}\lbrack \frac{{W( {s,t} )}U*( {s,t} )}{| {{W( {s,t} )}U*( {s,t} )} |} \rbrack}.}} & (16)\end{matrix}$

The value at each array point is the maximum magnitude of thecorresponding phase-correlation plane. It is computed using anincrementally rescaled and rotated correlation reference plane. Any oneof the color planes of the marked image usually suffices as the requiredarray u(m, n). Interpolating among the values of the three-dimensionalarray yields coordinates of the greatest-of-the-greatestphase-correlation maxima. From these coordinates, values of thehorizontal and vertical scale factors and angle of rotation of thecorrelation reference plane relative to the marked image are directlyread. The correlation reference plane is then rescaled and rotated tomore precisely align it with the manipulated marked image. A finalphase-correlation evaluation is made to determine the relativehorizontal and vertical offsets of the modified correlation referenceplane relative to the manipulated marked image. Finally, the entiremarked image is rescaled, translated and rotated in accordance with theinverses of the measured values to restore it to its original size andorientation. The thus modified marked image is now ready for use in thedetection and demonstration process to show the existence of thewatermark in the manipulated marked image.

In one embodiment the fine alignment of the correlation reference planerelative to the marked image is performed by evaluating athree-dimensional array of phase-correlation maxima, and theninterpolating within that array to find the location of the maximum ofthose maxima. The axes of the array are the horizontal magnification,vertical magnification and angular rotation that are systematicallyapplied to the correlation reference plane. All combinations of thefollowing incremental steps define the values of the coordinates of thearray. The vertical axis of w(m, n) is magnified/reduced from 96% to104% of its original size in 2% increments. In similar fashion thehorizontal axis of w(m, n) is magnified/reduced from 96% to 104% of itsoriginal size in 2% increments. Also in similar fashion w(m, n) isrotated relative to its original orientation from −5 degrees to +5degrees in 2 degree steps. At each combination of verticalmagnification, horizontal magnification, and angular rotation of thecorrelation reference plane, the phase-correlation plane p(m, n) isrecomputed as above. The maximum of the point values p(m*, n*) in theplane is stored into the three-dimensional array of phase-correlationmaxima at coordinates corresponding to each of the incrementallyadjusted values of vertical magnification, horizontal magnification, andangular rotation.

A flow diagram of this embodiment is shown in FIG. 6. Those skilled inthe art know there are many satisfactory algorithms available tomagnify/reduce and rotate digitized images. Any one of those algorithmscan be used for manipulation of the correlation reference plane in thefollowing description. As described above, the discrete Fouriertransform of the marked image U(s, t) is formed, 602. Initial values areset for stepping variables vertical magnification, Vm=0.96, horizontalmagnification, Hm=0.96, and angular rotation, Ar=−5°, 604. Thecorrelation reference plane is vertically magnified/reduced according toVm, 606. The so adjusted plane is then horizontally magnified/reducedaccording to Hm, 608. The so adjusted plane is then rotated according toAr, 609. The discrete Fourier transform of the so adjusted plane W(s, t)is formed, 610. The phase-correlation plane p(m, n) is calculated usingthe relationship of equation (16), 611. The p(m, n) plane is examined tofind the coordinates (m*, n*) of its maximum value, 612. The coordinates(m*, n*) and p(m*, n*) are stored in the three-dimensional array beingformed. The three-dimensional array is indexed by Vm, Hm and Ar, 613.The value of Ar is examined, 614. If it is less than plus five degrees,it is incremented by plus two degrees, 615, and steps 609–614 arerepeated until Ar is found to be plus five degrees in step 614. When Aris found to be plus five degrees in step 614, the value of Hm isexamined, 616. If Hm is less than 1.04, it is incremented by 0.02 and Aris reinitialized to minus five degrees, 617. Steps 608 to 616 arerepeated until Hm is found to be 1.04 in step 616. When Hm is found tobe 1.04, Vm is examined, 618. If Vm is found to be less than 1.04, it isincremented by 0.02, and Ar is initialized to minus five degrees, and Hmis initialized to 0.96, 619. Steps 606 to 618 are repeated until Vm isfound to have a value of 1.04 in step 618. When Vm is found to be equalto 1.04, the values of the three-dimensional array are interpolated tofind the maximum of the maxima peaks, 620. The resulting coordinates ofthe maximum of maxima peaks provide the final values for the verticalmultiplier, the horizontal multiplier and the rotational angle for bestalignment of the manipulated marked image with the correlation referenceplane. The corresponding resulting values of m* and n* of the maximum ofmaxima provide the offset displacements of the manipulated marked imagerelative to the correlation reference plane. The manipulated markedimage is then rescaled by the inverses (reciprocals) of the foundvertical and horizontal multipliers. It is rotated by the inverse(negative) of the found angular rotation, and is offset by the inverses(negatives) of m* and n*, 622. This completes the fine setting processof reorienting and resizing.

It will be apparent to those skilled in the art that either thecorrelation reference plane or the manipulated marked image can beresized and reoriented to bring one into alignment with the other. Thepreferred embodiment resizes and reorients the manipulated marked imageto bring it into alignment with the correlation reference plane, andhence into element-to-element alignment with the watermarking plane.

Detecting the Watermark in a Marked Image

The process of watermark detection is designed to produce a visiblyrecognizable small image as its end product. The recognizable endproduct is obtained in a procedure which depends upon the existence andknowledge of the watermark based on the robust random sequence. Theprocess exploits the extremely sophisticated and not yet completelyunderstood pattern recognition capabilities of the human visual system.It is through this exploitation that defeating the imparted watermarkbecomes much more difficult. A small rectangular array, called aselector, is conceived to implement the detection process. The selectorarray size must be much smaller than the pixel array of the marked imageto which it is being applied. This is to allow overlaying the selectoron the image hundreds of times without overlapping. The selector arrayshould be made large enough that a pixel array having the samedimensions could contain a recognizable binary image. More complexembodiments use a color rather than binary image as a reference. Aselector having 32 rows and 128 columns is used in an embodimentdescribed herein. It is applied to a marked image that has more than onemillion pixels.

The selector is used to locate rectangular clusters of pixels in themarked image and corresponding clusters of elements in the reconstitutedwatermarking plane. The clusters are randomly scattered non-overlappingpositions. Random scattering of the clusters is done to furtherfrustrate attempts to defeat watermark protection. Each element of theselector contains one or more devices associated with variables thatserve to store partial results of the watermark detection scheme. Oneembodiment uses two selector devices, one called a “coincidence counter”and the other a “non-coincidence counter.” All coincidence counters andnon-coincidence counters are set to a zero value before the detectionprocess is begun.

A variable, called a statistically related variable, is defined whichstatistically relates an attribute of an element being considered to theattributes of its neighboring elements. For each pixel in the markedimage a first variable is computed for that pixel and a second variableis computed for that pixel's corresponding element in the reconstitutedwatermarking plane. A positive test results when the computed firstvariable has the same result, or a nearly or statistically deemedequivalent result, as the computed second variable. If the results aredeemed to be different, the test result is deemed to be negative. Thefirst variable is recomputed and compared with the second variable foreach of that pixel's color planes. The coincidence counter associatedwith that selector element is incremented by unity for each color planeproducing a positive result and the non-coincidence counter isincremented by unity for each color plane that produces a negativeresult. The purpose of each element's coincidence and non-coincidencecounters is to associate with that element a confidence level of thewatermark's identification with the random sequence known only to themarker and/or the marking entity. The quantified confidence level foreach element is derived from the values in that element's coincidenceand non-coincidence counters, and is called a coincidence value.

For a tristimulus color image and for each cluster of pixels, the rangeof each coincidence counter value is from zero to plus three. A zero isobtained if the test results were negative for all three color planes. Aplus three is obtained if the test results were positive for all threeplanes. The range of each non-coincidence counter is also from zero toplus three, but conversely, a zero is obtained if the test results forall three planes were positive and a plus three is obtained if the testresults of all three planes were negative. The count in each coincidencecounter is the accumulated sum of the counts of positive results forcorresponding pixels at each cluster location, and the count in eachnon-coincidence counter is the accumulated sum of the counts of negativeresults for corresponding pixels at each cluster location. A coincidencecounter value larger than the value of its corresponding non-coincidencecounter is associated with a partial watermark detection. A composite ofcoincidence counter values greater than their correspondingnon-coincidence counter values for a preponderance of the selector'selements results from and corresponds with a detected watermark having ahigh confidence value.

In an embodiment the test results and/or the comparison are performed bysubtraction operations. In a particular embodiment the attribute used isthe pixel's brightness values. The statistical relationship is in regardto the average brightness value of the neighboring pixels. In this case,watermark detection proceeds with the steps shown in FIG. 7. A selectorarray size is selected, 702. In this example, the selector array size is32 by 128 elements. All the coincidence and non-coincidence counters areinitialized by setting them to read zero, 704. A specified particularelement of the selector is placed on an initial position of the expandedwatermarking plane, 706. The particular first element is often theselector element that is at its upper leftmost corner. This particularelement also locates a corresponding pixel and its components in all thecolor planes of the marked image when the marked image is aligned withthe expanded watermarking plane.

The following portion of the detection schema is repeated iterativelyfor all selector elements, for all color planes of each pixel, and forall selected clusters. The next two eight-bit integers are chosen fromthe regenerated robust random sequence, 708. When the schema is startedfor the first selector element, the next two eight-bit integers chosenin this step 708 are actually the first two eight-bit integers of therobust random sequence. The two eight-bit integers are scaled to formrandom horizontal and vertical offsets from the initial or previousselector location, and the selector is moved to that position, 710. Theselector element sequence is reset to the coordinates of the initialparticular selector element, 711. This selector element is used tolocate the corresponding particular element in the watermarking plane,712. The average magnitude of its neighboring elements in thewatermarking plane is computed, 713. In the example, this is the averageof the magnitudes of the particular element's neighbors that lie in an11 by 11 square of elements with the particular element at the center ofthe square. If the selector element is too near an edge of thewatermarking plane to be at the center of its neighborhood, the squareneighborhood is moved to encompass the particular element's nearest 120existing neighbors.

The next color plane is chosen, 714. In the beginning of this iterativeschema this next color plane is actually the first color plane. In thecase of a monochrome image this is the only color plane. The coordinatesof the particular selector element are used to locate a correspondingpixel color component in this next color plane, 715. The averagebrightness of the neighboring 120 pixel color components is computed,716, in a manner identical to that stated above for watermarking planeelements. The values of the particular watermarking plane element andthe corresponding pixel color component are compared to their respectiveneighborhood averages. If both values are equal to or greater than theirrespective neighborhood averages, 717, or if both values are less thantheir respective neighborhood averages, 718, the coincidence counter ofthat particular selector element is incremented, 719 a. If one value isless than its respective neighborhood average and the other value isequal to or greater than its respective neighborhood average, thenon-coincidence counter of that particular selector element isincremented, 719 b. The magnitude of the value in each coincidencecounter relative to the magnitude of the value in its correspondingnon-coincidence counter is associated with the probability of watermarksequence validation.

A determination is made if all color planes were chosen for testingtheir corresponding brightness value with regard to its neighboringaverage, 720. If not, the process returns to step 714 for choosing thenext color plane. Steps 715 to 720 are repeated for this color plane.This is continued until step 720 indicates the all color planes aretested. When the last (or only) color-plane is tested, a determinationis made if every element for that selector was chosen, 724. If not, thenext selector element is chosen, 726. Generally, the next element is thenext right-wise adjacent element on that row. If there is no nextadjacent element on that row, the next element is the left-most elementin the next selector row. This next selector element becomes the newparticular element. Steps 712–724 are repeated until all selectorelements are chosen and tested. When it is determined in step 724 thatall elements have been chosen, a determination is made if allnon-overlapping selector locations have been chosen, 728. If not, steps708 through 728 are repeated for all selector elements and marked imagecolor planes. When it is determined in step 728 that all selectorlocations are tested, all coincidence counters have their test resultvalues.

FIG. 8 shows a random multiple totality of positions of the selector 810in a selector plane 802 resulting from an implementation of the processof FIG. 7. FIG. 8 shows a watermarking plane 804 and three color planes806–808 of the marked image. The first selector element acted upon isoften the top leftmost element 812 of the selector in each of theselector positions. It is noted that although each selector position israndomly offset from previously chosen positions, the positions do notoverlap each other.

The values contained within each coincidence and non-coincidence counterassociates with their corresponding selector element a confidence levelof the watermark's identification with the random sequence known only tothe marker and/or the marking entity. The watermark is considered to bedetected if a preponderance of the differences of coincidence countervalues less their respective non-coincidence counter values are nonnegative. Thus, an examination of the totality of these non negativedifferences explicitly suffices for declaring the watermark detected ornot detected. Indeed, this can be considered as the end of the watermarkdetection technique.

Those skilled in the art will recognize that it is possible tomathematically derive a “probability of watermark detection,” in whichthe “probability of watermark detection” is greater than zero and lessthan one (where a value zero represents certainty of the absence of awatermark and a value one represents certainty of its presence), basedonly on the coincidence and non-coincidence counter values and assumingonly the property of uniform distribution of the random brightnessmultiplying factors. However, alternative embodiments recognize that a“preponderance” of differences being non negative is an inexact measure,at best. Clearly, if only a simple majority of the differences are nonnegative, whether the watermark is detected or not is at best a judgmentcall. Most likely it would be conceded as not having been a detection.To assist in this judgment, the present invention exploits the abilityof the human visual system to recognize a pattern in a cluttered field.This is accomplished by forming a binary image called a visualizer. Thevisualizer is formed to have the same dimensions as the selector (e.g.,32×128 pixels). A clearly recognizable pattern is placed into thevisualizer. A typical visualizer pattern is shown in FIG. 9, 900. Theblack border surrounding the visualizer is not considered to be part ofthe visualizer pattern. The pattern is an arrangement of blocks of blackand white pixels forming an easily recognizable pattern. A typicalpixel, 902, is at the lower ending of the image of a C. The visualizerimage is entirely white except for pixels making the letters IBM, 904,the copyright logo, 906, and the visualizer frame, 908.

The visualizer pattern is used to provide a visual image of the actualdegree of “preponderance” of coincidence counters being non negative.The method steps diagrammed in FIG. 10 are used to provide a watermarksignature in relation to the visualizer pattern. The watermark signatureis derived by using the visualizer pattern in combination with thecoincidence counter difference data to form what is herein referred toas the ‘visualizer-coincidence image’.

In one embodiment, the visualizer-coincidence image is formed with thesteps shown in FIG. 10. A visualizer pattern is formed having a pixelarray equal in size to the element array of the selector, 1002. Thevisualizer array consists of white and black pixels, where white isgiven the value one and black the value zero. All elements of theselector array will be examined to determine the pixel content of thevisualizer-coincidence image. To do this, the selector element sequenceis reset and the first element of the sequence is chosen, 1004. For thechosen selector element, the count in its corresponding non-coincidencecounter is subtracted from the count in its corresponding coincidencecounter, forming a difference, 1006. The sign of the difference istested, 1008, and if it is negative the corresponding pixel of thevisualizer is inverted (white is changed to black, and black to white)and placed into the corresponding pixel of the visualizer-coincidenceimage, 1010 b. If the sign is positive, the corresponding pixel of thevisualizer is placed unmodified into the corresponding pixel of thevisualizer-coincidence image, 1010 a. The selector element sequence istested to see if all elements have been chosen, 1012, and if not, thenext element is chosen, 1014, and steps 1006 to 1012 are repeated. Ifall selector elements have been chosen, the visualizer-coincidence imageis displayed, 1016. A judgment is made as to whether the pattern in thevisualizer-coincidence image is recognized as a reproduction of thevisualizer pattern, 1018. If it is recognized, the watermark ispositively detected, 1020 a. If not, the watermark is not detected, 1020b.

It is evident to those skilled in the art that if only the sign of thedifference between the count in a coincidence counter less the count inits corresponding non-coincidence is to be used in constructing thevisualizer-coincidence image, then only one counter would have beenneeded for each selector element. In that case, step 719 a of FIG. 7would read “Increment the counter of Selector's Element,” and step 719 bwould read “Decrement the counter of Selector's Element.”

FIG. 11 shows a detection, 1102, resulting from the visualizer of FIG. 8for an imparted watermark made at a modulation strength of 1%. Aspreviously stated in all cases the black border is not part of thevisualizer-coincidence image. A stronger replication of the visualizer,1202, resulting for an imparted watermark made at a modulation strengthof 2% is shown in FIG. 12. A still stronger replication of thevisualizer, 1302, resulting for an imparted watermark made at amodulation strength of 4% is shown in FIG. 13.

An attempt to detect a watermark in an image that does not have one, orin an image for which the watermarking plane cannot be reconstituted,produces a visualizer pattern that is an unrecognizable random melee.FIG. 14 shows a typical visualizer-coincidence image, 1402, when awatermark is not detected. This results when many visualizer pixels aresubjected to inversion. A preponderance of pixels not requiringinversion indicates watermark detection. This method in fact has anextremely low probability of false-positive detection. Even in a highlytextured marked image, the visualizer pattern should be clearlyrecognizable to signify a watermark detection of very high credibility.

Clearly, more information is present in the coincidence andnon-coincidence counter values than has been exploited above, where onlythe algebraic sign of their difference has been used. An alternativemethod of converting the visualizer image into a visualizer-coincidenceimage uses the magnitude of each coincidence counter value and that ofits corresponding non-coincidence counter. If C(i′, j′) is the value ofthe coincidence counter associated with selector element i′, j′ andC′(i′, j′) is the value of the corresponding non-coincidence counter,then the normalized magnitude of their difference e(i′,j′) is:(i′, j′)=C(i′j′)/[C(i′, j′)+C′(i′, j′)]  (17)whenC(i′, j′)+C′(i′, j′)>0,  (18)and:e(i′, j′)=1/2,  (19)whenC(i′,j′)+C′(i′, j′)=0.  (20)

In this case, the visualizer image is converted into avisualizer-coincidence image by replacing each pixel in the visualizerimage with the corresponding value of e(i′, j′), when the visualizerpixel value is one; and by 1−e(i′, j′), when the visualizer pixel valueis zero. Notice that the visualizer-coincidence image is no longer abinary image, but includes gray shades ranging from black to white. Thejudgment as to whether the pattern placed in the visualizer isrecognizable in the visualizer-coincidence image is the same as before,and an attempt to detect the presence of a known watermark in an imagenot having one, or in an image having one but for which the watermarkingplane cannot be precisely reconstituted, also still produces anunrecognizable random melee in the visualizer-coincidence image.

Thus, this scheme makes more use of the actual values in the coincidenceand non-coincidence counters. It still employs a black and white elementvisualizer image pattern wherein each element is either black or white(zero or one). However, the resulting elements of thevisualizer-coincidence image have values ranging between zero and onesuch that when displayed it has various levels of shades of gray. Thegray level depends on the counter data.

An embodiment of this alternative scheme is shown in FIG. 15. Avisualizer pattern is formed having a pixel array equal in size to theelement array of the selector, 1502. The visualizer array consists ofwhite and black pixels, where white is given the value one and black thevalue zero. All elements of the selector array will be examined todetermine the pixel content of the visualizer-coincidence image. To dothis, the selector element sequence is reset and the first element ofthe sequence is chosen, 1504. For the chosen selector element, the ratioof the count in its corresponding coincidence counter to the sum of theif counts in its corresponding coincidence and non-coincidence countersis computed, 1506. The color of the corresponding visualizer pixel istested, 1508, and if it is black, the ratio subtracted from one isplaced into the corresponding pixel of the visualizer-coincidence image,1510 a. If the visualizer pixel is white, the ratio is placed unmodifiedinto the corresponding pixel of the visualizer-coincidence image, 1510b. The selector element sequence is tested to see if all elements havebeen chosen, 1512, and if not, the next element is chosen, 1514, andsteps 1506 to 1512 are repeated. If all selector elements have beenchosen, the visualizer-coincidence image is displayed as a high contrastmonochrome image, 1516. A judgment is made as to whether the pattern inthe visualizer-coincidence image is recognized as a reproduction of thevisualizer pattern, 1518. If it is recognized, the watermark ispositively detected, 1520 a. If not, the watermark is not detected, 1520b.

The Implementation of Brightness Modification by Addition Instead ofMultiplication

An alternative, and equivalent, form for modifying pixel brightness isto change the brightness by adding to or subtracting from the componentY(i, j) a different small random value ε(i, j). As before stated, 1≦i≦Iand 1≦j≦J are the row and column indices of the pixel location in theimage. To help make the brightness variation less visible, ε(i, j) ismade proportional to the original brightness of the component, therebymaking the change smaller in darker areas of the image where the humaneye is more discerning of changes in brightness. Thus, ε(i, j)=δ(i,j)Y(i, j), where δ(i, j) is a value selected from an array of randomvalues that may have the range −0.5<δ(i, j)<0.5. The modified componentY′(i, j)=Y(i, j)+ε(i, j)=Y(i, j)+δ(i, j)+δ(i, j). To alter only thebrightness of each pixel in a color image, the ratios of its componentsmust be preserved. If the color components of the unaltered pixel areX(i, j), Y(i, j), and Z(i, j), and the color components of thebrightness altered pixel are X′(i, j), Y′(i, j), and Z′(i, j), thenX′(i, j)/X(i, j)=Z′(i, j)/Z(i, j)=Y′(i, j)/Y(i, j)=1+δ+(i, j). It isevident that this is equivalent to multiplying the brightness of theeach color component by 1+δ(i, j), since X′(i, j)=X(i, j)[1+δ(i, j)],Z′(i, j)=Z(i, j)[1+δ(i, j)], and Y′(i, j)=Y(i, j)[1+δ(i, j)]. If therandom values 1+δ(i, j) are set equal to w(i, j) as defined before, thetwo methods are identical. In summary, the modification of pixelbrightness by an additive value that is proportional to pixel brightnesswhile preserving the ratios of the color components of the pixel isequivalent to modifying the brightness of the pixel by multiplication.An additive and multiplicative modulation can have a different effectonly if the ratios of the color components of the pixel are allowed tochange.

Using a Blurring Filter Before Attempting Watermark Detection to Improvethe Probability of Detection

Watermark detection may be enhanced in accordance with the presentinvention as described hereinafter in a manner that is adaptable for useof any of many watermarking techniques. It is most particularlyadaptable to a watermarking technique employing a watermarking plane.Thus, although the enhancement of the detection technique is adaptableto many watermarking techniques, it is most easily described andadaptable to the watermark imparting and detecting methods describedpreviously herein.

As described above for particular embodiments, watermarks are impartedinto an image by multiplying the components of each pixel of the imageby the linearly remapped values of the watermarking plane, w(i, j),where 1>w(i, j)≧(1−2β), i is the value's row index, j is the value'scolumn index, and β is the modulation strength of the watermark.Additionally, all elements in the generated watermarking plane, treatedas an ensemble, are adjusted to have a mean and median of 1−β. In otherwatermark embodiments this is accomplished by addition and/orsubtraction operations.

A method for improving the detection of the imparted watermark in amarked image and, more specifically, in a derived copy of a marked imageemploys use of a two-dimensional blurring filter prior to an attempteddetection. A blurring filter is also called a low-pass filter insignal-processing terminology. Application of the blurring filter isadvantageous in that it reduces high-frequency noise content among thecolor components in the marked image while leaving low-frequency contentrelatively unaltered.

In the example embodiment, since the watermark, as imparted into theimage, has the appearance and behavior of a two-dimensional noisepattern itself, any addition of high-frequency noise can potentiallypartially obscure the watermark and make it more difficult to detect.This is specifically the case if a derived copy is produces by scanninga printed copy of a marked image. Substantial high-frequency noise isadded to a marked image by the screening process used in preparation forits printing. Printing ordinarily is accomplished with one or severalinks or dyes that each have an invariable color. The screening processproduces various shades of the invariably colored inks or dyes, neededto reproduce the color components, by covering the spatial arearepresented by each pixel with a finer grids of dots of the inks ordyes. Each of the grids of dots has a varying spatial density of theinks or dyes, and each dot in a grid of dots is significantly smallerspatially than the pixel area. The grids of dots so produced, one foreach color component, spatially replace the pixel they represent in theprinted image copy, and, after fusion by the human viewing system,collectively produce a perceived correct color of the pixel.

The screening process, by converting the components of each pixel intogrids of dots of still smaller dimensions, inherently addshigh-frequency artifacts and noise to the printed image copy that werenot in the original image. This can be verified easily by viewing aprinted image under moderate magnification. If the printed image is thenscanned to produce a derivative digitized image, the addedhigh-frequency noise reproduced in the derivative copy is detrimental towatermark detection. It is to reduce the detrimental effects of theadded high-frequency that a blurring filter is used. As stated above inthe subsection titled “The Property of Explicit Low Frequency Content”the watermarking plane is designed to have significant low frequencycontent and will thus be relatively immune to the action of a blurringfilter, but the high-frequency content of image, and more importantlythe added noise, will be substantially attenuated.

An example rudimentary blurring filter can be implemented in thefollowing manner. Each color plane of the image, represented as arectangular array of like color components, is partitioned, right toleft and top to bottom, into small sub-arrays that are three pixels highand three pixels wide. If the number of pixels in a row or column of theimage array is not evenly divisible by three, the edge sub-arrays at theright or bottom of the partitioned image will contain fewer than ninepixels. The color components of the nine pixels in each sub-array (orfewer than nine if the sub-array is an edge sub-array) are averaged. Theaverage value of the color components in each sub-array is then used toreplace all the values in that sub-array. This completes thetwo-dimensional blurring filter. Those skilled in the art will recognizethat there many other more sophisticated ways to implement atwo-dimensional blurring filter. Nevertheless, in the method of thepresent invention the important desired result of applying any blurringfilter remains the same as the that of applying the rudimentary filterdescribed here, namely, the reduction of high spatial frequencies andthe preservation of low spatial frequencies of features in thederivative image.

In the example rudimentary blurring filter presented, the first step ofthe method was to divide a marked image's color plane into nine elementsquare sub-arrays. The choice of the size of the sub-arrays determinesthe degree to which high spatial frequencies among the pixel componentsin the marked image are reduced in the filtered image, if the markedimage contains such high spatial frequencies, which it may not. By usingnine element sub-arrays, the highest spatial frequency that can possiblyexist in the filtered image is reduced by a factor of three. The largerthe sub-array is chosen, the greater is the reduction of the highestpossible spatial frequency that can exist in the filtered image. It willbe apparent to those skilled in the art that, when applying a blurringfilter, the degree to which the highest spatial frequency is to bereduced depends upon the degree to which high-frequency content in thewatermarking plane used to produce the marked image was reduced. If theobjective of using the blurring filter it to improve watermarkdetection, it would become counter productive to reduce thehigh-frequency content of the marked image by a factor greater than thatused in creating the watermarking plane; to do so would remove not onlyundesirable high-frequency noise in the marked image but also some ofthe information contained in the imparted watermark.

Referring to FIG. 16, a highly enlarged segment of an examplewatermarked image is shown. The watermark was imparted according to themethod described previously herein. The modulation strength, β, used forthe marking was 2.5 percent and visibility of the watermark, even athigh magnification is classified as undetectable invisible. Referring toFIG. 17, a similarly enlarged segment of a derivative image is shown; itis derived from the marked image shown in FIG. 16 after it is screenedin preparation for printing, forming a screened image, and subsequentlyprinted and scanned. Note that significant high-frequency noiseresulting from the screening process is evident in FIG. 17. FIG. 18shows a filtered image produced by applying the rudimentary blurringfilter to the derived image. The noise reduction resulting fromapplication of the blurring filter is evident by comparing FIG. 18,after the application, with FIG. 17, before the application.

Watermark detection was attempted for each of the three images, theenlarged segments of which are shown in FIGS. 16, 17, and 18. Thewatermark visualizer-coincidence images realized form the detectionusing the original marked image is shown in FIG. 19. The detection is aperfect detection. The original marked image is then screened forprinting, printed and scanned to form the derivative image. Thewatermark visualizer-coincidence image realized form the detection usingthe derivative image is shown in FIG. 20. The detection is very weak,nearly nonexistent. After the rudimentary blurring filter is applied tothe derivative image to form the filtered image, watermark detection isagain attempted. The watermark visualizer-coincidence image realizedform the detection using the filtered image is shown in FIG. 21. Thedetection, although imperfect, is very strong, testifying to theefficacy of the use of the blurring filter before attempting watermarkdetection.

Use of a blurring filter is advantageous before any attempted watermarkdetection, regardless of the robust watermarking method used. If awatermark is robust, that is, if it is resistant to attacks, it mustordinarily contain significant low-frequency content. The low-frequencycontent of the watermark will not be unduly disturbed by the blurringfilter, since the blurring filter is by its nature a low-pass filter.Any detection-disturbing high-frequency content in the image, whetheroccurring naturally as a part of the image or whether added byartificial means, such as screening in preparation for printing, will besuppressed by the action of the blurring filter. The actual amount ofblurring is generally dependent upon the particular application and/orwatermark. This is determined in ways known to those skilled in the art.

Although the description is made for particular embodiments, techniquesand arrangements, the intent and concept of the present invention aresuitable to other embodiments, techniques and arrangements. For example,an obvious choice, and the choice of last resort, in demonstrating theexistence of a watermark in a manipulated marked image is to againimpart the watermark onto a copy of the unmarked original digitizedimage, and to use the color planes of that reconstituted marked image asideal substitutes for the watermarking plane. The disadvantage of thisalternative method is that it requires access to a copy of the unmarkedoriginal image. The visualizer can also have multiple color planes. Thevisualizer can be employed without the selector by having at least onestatistical value associated with each pixel of the visualizer. Also,sequential repositioning of the selector on the reconstitutedwatermarking plane need not be non-overlapping. Non-overlapping selectorpositions in the presented embodiment represent only a computationalsimplification. Also, a small random but coherent image may be includedin the watermarking plane at positions known only to the marker and/ormarking entity; if the so constituted watermarking plane were impartedonto a uniform color plane with strong modulation strength, the coherentimage would be visible without use of a visualizer. Other methods ofwatermark detection and/or demonstration may be employed. These may forinstance utilize any of the many statistical relationships betweenelements and their neighbors or non-neighbors. The robust techniquespresented here may be used in combination with visible watermarkingtechniques as well as fragile invisible techniques. It will be clear tothose skilled in the art that other modifications to the disclosedembodiments can be effected without departing from the spirit and scopeof the invention.

The present invention can also be realized in embodiments of anapparatus having mechanisms for implementing the methods of the presentinvention as described herein in manners known to those skilled in theart. For example, the present invention can also be realized as anapparatus to impart a watermark onto a digitized image, said apparatuscomprising: means for providing a digitized image having at least oneimage plane, said image plane being represented by an image array havinga plurality of pixels, said pixel having at least one color component,said watermark being formed using a distinct watermarking planerepresented by an array having a plurality of distinct watermarkingelements, each of said distinct watermarking elements having an arrayposition and having one-to-one positional correspondence with said imagepixels; and means for multiplying said brightness data associated withsaid at least one color component by a predetermined brightnessmultiplying factor, wherein said brightness multiplying factor is acorresponding distinct watermarking element, said distinct watermarkingelement being in the domain of 0.5 to 1.0. Thus in an embodiment thepresent invention can also be realized as an apparatus for imparting awatermark onto a digitized image comprising the steps of: means forproviding said digitized image comprised of a plurality of pixels,wherein each of said pixels includes brightness data that represents abrightness of at least one color; and means for multiplying saidbrightness data associated with at least one of said pixels by apredetermined brightness multiplying factor in the domain of 0.5 to 1.0.In a particular embodiment of the apparatus the image has I rows and Jcolumns, and has a pixel in row i and column j having a brightness Y(i,j), and the means for multiplying includes: means for adding to orsubtracting from the brightness Y(i, j) a different small random valueε(i, j), wherein 1≦i≦I and 1≦j≦J are the row and column indices of apixel location in the image.

Thus in an embodiment the present invention can also be realized as anapparatus for imparting a watermark onto a digitized image comprising:means for providing said digitized image comprised of a plurality ofpixels, wherein each of said pixels includes brightness data thatrepresents a brightness of at least one color, with said image having Irows and J columns, and a pixel in row i and column j having abrightness Y(i, j); and means for adding to or subtracting from thebrightness Y(i, j), for all i and all j, a random value ε(i, j), wherein1≦i≦I and 1≦j≦J are the row and column indices of a pixel location inthe image.

Thus in an embodiment the present invention can also be realized as anapparatus for generating a watermarked image, the apparatus comprising:means for imparting a watermark onto a digitized image having aplurality of original pixels, each of said pixels having originalbrightness values; means for providing said digitized watermarking planecomprising a plurality of watermarking elements, each element having awatermark brightness multiplying factor and having one-to-one positionalcorrespondence with said original pixels; and means for producing awatermarked image by multiplying said original brightness values of eachof said original pixels by said brightness multiplying factor of acorresponding one of said watermark elements.

Thus in an embodiment the present invention can also be realized as anapparatus comprising: means for forming a watermarking plane including aplurality of elements each having a brightness adding or subtractingvalue; means for generating a robust random sequence of integers havinga first plurality of bits; means for linearly remapping said randomsequence to form a remapped sequence of brightness multiplying factorsto provide a desired modulation strength; means for computing a discreteFourier transform of said remapped sequence to form a Fourier sequencehaving frequency coordinates; means for expanding said frequencycoordinates to form an expanded sequence; means for computing an inverseFourier transform of said expanded sequence to obtain a watermarkingsequence of values; and means for deriving said brightness adding orsubtracting values of said elements of said watermarking plane basedupon said watermarking sequence of values.

Thus in an embodiment the present invention can also be realized as anapparatus for detecting a watermarking plane comprising: means forproviding an image having a plurality of pixels marked by thewatermarking plane, said watermarking plane having a plurality ofwatermarking elements; means for aligning said watermarking plane withsaid image; means for identifying a subset of said image pixels; meansfor each image pixel, u(i, j), wherein 1≦i≦I and 1≦j≦J, of said subsetof image pixels, including means for generating a first valuerepresenting a relationship between an attribute of said image pixelu(i, j) and an attribute of image pixels that neighbor said image pixelu(i, j); means for identifying a watermarking element w(i, j) thatpositionally corresponds to said image pixel u(i, j) and watermarkingelements that correspond to said image pixels that neighbor said imagepixel u(i, j); means for generating a second value representing arelationship between an attribute of said watermarking element w(i, j)and an attribute of the identified neighboring watermarking elements;and means for generating a coincidence value representing likelihoodthat said image is marked by said watermarking plane based upon saidfirst and second values.

Thus in an embodiment the present invention can also be realized as anapparatus comprising means for generating a visual representation of adata array of data elements having a data array size, including: meansfor providing a visualizer-coincidence pattern of visualizer-coincidenceimage pixels represented by a visualizer-coincidence array ofvisualizer-coincidence pixels, said visualizer-coincidence array havingan array size equal to said data array size, wherein each of saidvisualizer-coincidence pixels has a first color if a corresponding dataelement is a first logical value and a second color if saidcorresponding data element has a complementary logical value; means forsetting said visualizer-coincidence pixel to a first color if a value ofsaid data element is above a predetermined threshold and to anothercolor if said value is below said predetermined threshold; and means fordisplaying said visualizer-coincidence image to form said visualrepresentation.

Thus in an embodiment the present invention can also be realized as anapparatus for imparting a watermark onto a digitized image comprising:means for providing said digitized image comprised of a plurality ofpixels, wherein each of said pixels includes brightness data representedby at least one color component, Y; and means for adding to orsubtracting from said brightness data associated with at least one ofsaid pixels a predetermined brightness adding or subtracting factor inthe range of −0.5Y to +0.5Y, wherein said brightness adding orsubtracting factor has a relationship with a number taken from a randomnumber sequence, said relationship is a linear remapping to provide adesired modulation strength, and said modulation strength is less than50 percent.

Thus in an embodiment the present invention can also be realized as anapparatus for imparting a watermark onto a digitized image comprising:means for providing said digitized image comprised of a plurality ofpixels, wherein each of said pixels includes brightness data representedby at least one color component, Y; and means for adding to orsubtracting from said brightness data associated with at least one ofsaid pixels by a predetermined brightness adding or subtracting factorin the range of −0.5Y to +0.5Y, wherein said brightness adding orsubtracting factor has a relationship with a number taken from a randomnumber sequence, said relationship is a linear remapping to provide adesired modulation strength, said sequence is formed from a plurality ofrobust watermarking parameters, and said parameters comprise acryptographic key, two coefficients and an initial value of said randomnumber generator.

The present invention can be realized in hardware, software, or acombination of hardware and software. A visualization tool according tothe present invention can be realized in a centralized fashion in onecomputer system, or in a distributed fashion where different elementsare spread across several interconnected computer systems. Any kind ofcomputer system—or other apparatus adapted for carrying out the methodsand/or functions described herein—is suitable. A typical combination ofhardware and software could be a general purpose computer system with acomputer program that, upon being loaded and executed, controls thecomputer system such that it carries out the methods described herein.The present invention can also be embedded in a computer programproduct, which comprises all the features enabling the implementation ofthe methods described herein, and which—when loaded in a computersystem—is able to carry out these methods.

Computer program means or computer program in the present contextinclude any expression, in any language, code or notation, of a set ofinstructions intended to cause a system having an information processingcapability to perform a particular function either directly or aftereither or both of the following: conversion to another language, code ornotation, and/or reproduction in a different material form.

Thus the invention includes an article of manufacture comprising acomputer usable medium having computer readable program code meansembodied therein for causing a function described above. The computerreadable program code means in the article of manufacture comprisescomputer readable program code means for causing a computer to effectthe steps of a method of this invention. Similarly, the presentinvention may be implemented as a computer program product comprising acomputer usable medium having computer readable program code meansembodied therein for causing a function described above. The computerreadable program code means in the computer program product comprisescomputer readable program code means for causing a computer to effectone or more functions of this invention. Furthermore, the presentinvention may be implemented as a program storage device readable bymachine, tangibly embodying a program of instructions executable by themachine to perform method steps for causing one or more functions ofthis invention.

It is noted that the foregoing has outlined some of the more pertinentobjects and embodiments of the present invention. This invention may beused for many applications. Thus, although the description is made forparticular arrangements and methods, the intent and concept of theinvention is suitable and applicable to other arrangements andapplications. It will be clear to those skilled in the art thatmodifications to the disclosed embodiments can be effected withoutdeparting from the spirit and scope of the invention. The describedembodiments ought to be construed to be merely illustrative of some ofthe more prominent features and applications of the invention. Otherbeneficial results can be realized by applying the disclosed inventionin a different manner or modifying the invention in ways known to thosefamiliar with the art.

1. A method for imparting a watermark onto a digitized image, saidmethod comprising: providing a digitized image having at least one imageplane, said image plane being represented by an image array having aplurality of pixels, each pixel in said plurality of pixels having atleast one color component, said watermark being formed using a distinctwatermarking plane represented by an array having a plurality ofdistinct watermarking elements, each of said distinct watermarkingelements having an array position and having one-to-one positionalcorrespondence with said image pixels, and multiplying brightness dataassociated with said at least one color component by a predeterminedbrightness multiplying factor, wherein said brightness multiplyingfactor is a corresponding distinct watermarking element, and saidwatermark has a invisibility classification, wherein said brightnessmultiplying factor has a relationship with a number taken from a randomnumber sequence.
 2. A method as recited in claim 1, wherein saidrelationship is a linear remapping to provide a desired modulationstrength.
 3. A method as recited in claim 2, wherein said modulationstrength lies in the domain greater than or equal to zero and less thanor equal to 0.5.
 4. A method as recited in claim 1, wherein saiddistinct watermarking element, has a value being in the domain greaterthan or equal to zero and less than or equal to one.
 5. An apparatus toimpart a watermark onto a digitized image, said apparatus comprisingmechanisms for implementing the method of claim
 1. 6. A method forimparting a watermark onto a digitized image comprising the steps of:providing said digitized image comprised of a plurality of pixels,wherein each of said pixels includes brightness data that represents abrightness of at least one color; and altering said brightness dataassociated with a plurality of said pixels maintaining the hue andsaturation of said pixel, wherein said image has I rows and J columns,and has a pixel in row i and column j having at least one brightness,Y(i,j), and the step of altering includes: adding to or subtracting fromthe brightness Y(i,j) a different small random value e(i,j), whereinI<i<I and I<j<J are the row and column indices of a pixel location inthe image, and wherein color components of the unaltered pixel areX(i,j), Y(i,j), and Z(i,j), and color components of the brightnessaltered pixel are X′(i,j), Y′(i,j), and Z′(i,j), and the step of addingto or subtracting from includes setting e(i,j)=d(i,j)Y(i,j), whered(i,j) is a value selected from an array of random values within a rangeof 0<=d(i,j)<=1, such that the modified brightnessY′(i,j)=Y(i,j)+e(i,j)=Y(i,j)+d(i,j)Y(i,j), andX′(i,j)/X(i,j)=Z′(i,j)/Z(i,j)=Y′(i,j)/Y(i,j)=e(i,j)=1−d(i,j).
 7. Amethod as recited in claim 6, wherein the step of adding to orsubtracting from includes making e(i,j) proportional to an originalbrightness of the pixel.
 8. An apparatus for imparting a watermark ontoa digitized image comprising mechanisms for implementing the method ofclaim
 7. 9. A method as recited in claim 6, wherein the step of settingincludes preserving ratios of color components in each pixel.
 10. Amethod as recited in claim 9, wherein the step of preserving includessetting X′(i,j)/X(i,j)=Z′(i,j)/Z(i,j)=Y′(i,j)/Y(i,j)=1−d(i,j), whereinthe color components of the unaltered pixel are X(i,j), Y(i,j), andZ(i,j), and the color components of the brightness altered pixel areX′(i,j), Y′(i,j), and Z′(i,j).
 11. An apparatus for imparting awatermark onto a digitized image comprising mechanisms for implementingthe method of claim
 6. 12. An apparatus as recited in claim 11, whereinthe image is a marked image, and the mechanisms for implementingincludes means for altering said marked image employing a blurringfilter.
 13. A method for imparting a watermark onto a digitized imagecomprising the steps of: providing said digitized image comprised of aplurality of pixels, wherein each of said pixels includes brightnessdata that represents a brightness of at least one color, with said imagehaving I rows and J columns, and a pixel in row i and column j having abrightness Y(i,j); and for a plurality i and at least one j adding to orsubtracting from the brightness Y(i,j) a random value e(i,j), wherein 1I and J are the row and column indices of a pixel location in the image,wherein e(i,j) is in the domain 0 to 1 multiplied by Y(i,j).
 14. Amethod for detecting a watermark in a marked image, said methodcomprising: providing said marked image marked by a watermarking plane,said marked image having at least one color plane including a pluralityof image pixels, said watermarking plane having a plurality ofwatermarking elements, wherein each of said image pixels has at leastone brightness value and each of said watermarking elements has abrightness adding and/or subtracting factor, including the steps of: (a)reconstructing said watermarking plane; (b) aligning said watermarkingplane with said marked image such that each watermarking element has acorresponding image pixel; (c) providing a selector array and avisualizer image of equal size, wherein said selector array has aplurality of selector elements each having at least one counter, andwherein said visualizer image has a plurality of visualizer pixels eachhaving at least one brightness value, and wherein said visualizer pixelsrepresent a recognizable pattern when displayed; (d) resetting said atleast one counter to zero; (e) plating said selector in an initialposition by aligning said selector elements with a plurality ofcorresponding image pixels and a plurality of corresponding watermarkingelements; (f) choosing a selector element and identifying acorresponding watermarking element; (g) identifying a first plurality ofwatermarking elements that neighbor said corresponding watermarkingelement; (h) generating a first average tat represents an average ofbrightness adding and/or subtracting factors of said first plurality ofwatermarking elements; (i) choosing a color plane of said marked imageand finding a corresponding image pixel; (j) identifying a firstplurality of neighboring pixels that neighbor said corresponding imagepixel; (k) generating a second average that represents an average ofbrightness values of said first plurality of neighboring pixels; (l)updating said at least one counter based upon first and secondcomparison operations, wherein said first comparison operation comparessaid first average with said brightness adding and/or subtracting factorof said corresponding watermarking element and said second comparisonoperation compares said second average with said brightness value ofsaid corresponding pixel; (m) repeating steps (i) through (l) for allcolor planes; (n) repeating steps (f) through (m) for all selectorelements; (o) choosing a new selector position that does not overlap anyprevious selector position; (p) repeating steps (f) through (o) for allnon-overlapping selector positions; and (q) generating a visualrepresentation indicating detection of said watermark in said markedimage utilizing said at least one counter of said selector array andsaid visualizer pixels, wherein the step of aligning said watermarkingplane with said marked image includes altering said marked imageemploying a blurring filter.
 15. An apparatus for detecting a watermarkin a marked image comprising mechanisms for implementing the method ofclaim
 14. 16. A method for detecting a watermarking plane comprising thesteps of: providing an image having a plurality of image pixels, u(i,j),with said image having I rows and J columns, and a pixel in row i andcolumn j having at least one component, marked by a watermarking plane;said watermarking plane having a plurality of watermarking elements,w(i,j), with said watermarking plane having I rows and J columns, and anelement in row i and column j having a brightness multiplying factor;aligning said watermarking plane with said image; identifying a subsetof said image elements; for each pixel, u(i,j), of said subset of imagepixels, generating a first value representing a relationship between anattribute of said pixel u(i,j) and an attribute of image pixels thatneighbor said pixel u(i,j); identifying a watermarking element, w(i,j),that corresponds to said pixel u(i,j) and watermarking elements thatcorrespond to said image pixels that neighbor said image pixel u(i,j);generating a second value representing a relationship between anattribute of said watermarking element w(i,j) and an attribute of theidentified watermarking elements; and generating a coincidence valuerepresenting a likelihood that said image is marked by said watermarkingplane based upon said first and second values.
 17. An article ofmanufacture comprising a computer usable medium having computer readableprogram code means embodied therein for causing detection of a watermarkin a marked image, the computer readable program code means in saidarticle of manufacture comprising computer readable program code meansfor causing a computer to effect the steps of claim
 16. 18. An articleof manufacture as recited in claim 17, wherein the image is a markedimage, and the step of aligning includes altering said marked imageemploying a blurring filter.
 19. A method as recited in claim 16,wherein the image is a marked image, and the step of aligning includesaltering said marked image employing a blurring filter.
 20. An apparatusfor detecting a watermarking plane comprising mechanisms for forimplementing the method of claim
 16. 21. A method for imparting awatermark onto a digitized image comprising the steps of: providing saiddigitized image comprised of a plurality of image pixels with saiddigitized image having I rows and J columns, and a pixel in row i andcolumn j having at least one component, Y(i,j); and adding to orsubtracting from said brightness data associated with at least one ofsaid pixels a predetermined brightness adding factor in the range of 0to Y(i,j), or brightness subtracting factor in the range of 0 to Y(i,j),wherein said brightness adding or subtracting factor has a relationshipwith a number taken from a random number sequence, said relationship isa linear remapping to provide a desired modulation strength, and saidmodulation strength is less than or equal to 50 percent.
 22. An articleof manufacture comprising a computer usable medium having computerreadable program code means embodied therein for causing a watermark tobe imparted onto a digitized image, the computer readable program codemeans in said article of manufacture comprising computer readableprogram code means for causing a computer to effect the steps of claim21.
 23. A method for imparting a watermark onto a digitized imagecomprising the steps of: providing said digitized image comprised of aplurality of image pixels with said image having I rows and J columns,and a pixel in row i and column j having at least one component, Y(i,j);and adding to or subtracting from said brightness data associated withat least one of said pixels by a predetermined brightness adding orsubtracting factor in the range of 0 to Y(i,j), wherein said brightnessadding or subtracting factor has a relationship with a number taken froma random number sequence, said relationship is a linear remapping toprovide a desired modulation strength, said sequence is formed from aplurality of robust watermarking parameters, and said parameterscomprise a cryptographic key, two coefficients and an initial value ofsaid random number generator.
 24. An article of manufacture comprising acomputer usable medium having computer readable program code meansembodied therein for causing a watermark to be imparted onto a digitizedimage, the computer readable program code means in said article ofmanufacture comprising computer readable program code means for causinga computer to effect the steps of claim
 23. 25. An apparatus forimparting a watermark onto a digitized image comprising mechanisms forimplementing the method of claim
 23. 26. A method for detecting awatermark, said method comprising: providing a marked image having aplurality of image pixels said marked image being marked by awatermarking plane, having a plurality of watermark elements; aligningsaid watermarking plane with said marked image, and generating acoincidence value by averaging a detection coincidence for each selectorelement of a group of selector elements taken from said image pixels.27. A method as recited in claim 26, wherein each of said group ofselector elements has a selector size, said method further comprising:providing a visualizer pattern having a plurality of visualizer pixelsand a visualizer size equal to said selector size, each of saidvisualizer pixels being associated with one of said selector elementsand having a visualizer color; and displaying a watermark detectionpattern having a size at least equal to said visualizer size and aplurality of visualizer-coincidence pixels, wherein each of saidvisualizer-coincidence pixels is associated with a correspondingselector element and a corresponding visualizer pixel, and each of saidvisualizer-coincidence pixels being displayed having said visualizercolor when said coincidence value of said corresponding selected elementhas an indication of a detection success and having another colorotherwise.
 28. A method as recited in claim 26 wherein said watermark isbased on a factor multiplying a brightness value of each of said imagepixels.
 29. A method as recited in claim 26, further comprising:reconstructing said watermarking plane used in generating saidwatermark.
 30. A method as recited in claim 29, wherein saidwatermarking plane has a plurality of watermarking elements, said methodfurther comprising: rotating, resizing and said image to bring it to asize and position of an original image, and aligning said watermarkingplane with said marked image such that each of said watermarkingelements has a corresponding image pixel.
 31. A method as recited inclaim 26, wherein each said group contains 128 elements.
 32. A method asrecited in claim 26, wherein each pixel of said image pixels has amonochrome brightness value.
 33. A method as recited in claim 26,wherein said watermarking plane is generated using a plurality of robustwatermarking parameters.
 34. A method as recited in claim 26, whereinsaid coincidence value is determined using a statistically relatedattribute relating each said selector element to a plurality ofneighboring elements.
 35. A method as recited in claim 34, wherein saidattribute is a brightness value.
 36. An article of manufacturecomprising a computer usable medium having computer readable programcode means embodied therein for causing detection of a watermarkimparted onto a digitized image, the computer readable program codemeans in said article of manufacture comprising computer readableprogram code means for causing a computer to effect the steps of claim26.
 37. A method as recited in claim 26, wherein the image is a markedimage, and the step of aligning includes altering said marked imageemploying a blurring filter.
 38. An apparatus for detecting a watermarkcomprising mechanisms for implementing the method of claim
 26. 39. Amethod for detecting a watermark imparted on an image, said methodcomprising: providing said image having at least one image plane, saidimage plane being represented by an image array having a plurality ofimage elements, said watermark being formed using a watermarking planerepresented by a watermarking array having a plurality of watermarkingelements, each of said watermarking elements having a first arrayposition and having one-to-one positional correspondence with said imageelements; computing a first statistically related variable for eachelement of at least one first grouping of a first selector array ofelements taken from said image elements, wherein each of said imageelements has a second array position; computing a second statisticallyrelated variable for each element of at least one second grouping of asecond selector array of elements taken from said watermarking elements,wherein each element of said second selector array of elements hasone-to-one positional correspondence with said first selector array, andwherein said correspondence forms combinations of correspondingelements; comparing to determine an affirmative and non-affirmativelikeness of said first and second statistically related variables foreach of said combinations of corresponding elements; and forming atleast one comparison array having one-to-one correspondence with said atleast one first grouping and having a plurality of comparison elements,wherein each of said comparison elements contains a positive detectionindication for each element of said first grouping when said step ofcomparing results in an affirmative likeness, and a negative detectionindication for each element of said first grouping when said step ofcomparing results in a non-affirmative likeness.
 40. A method as recitedin claim 39, wherein said watermark is formed by adding or subtracting abrightness factor of each of said image elements by an amount containedin a corresponding element of said watermarking elements.
 41. A methodas recited in claim 39, wherein said first grouping corresponds to aselector positioned to encompass said first selector array of elementsforming a rectangular cluster of elements.
 42. A method as recited inclaim 39, wherein said first statistical variable is formed by comparingan attribute of said each element of said first selector array ofelements to an average attribute of its 128 closest neighbors.
 43. Amethod as recited in claim 42, wherein said attribute is a ratio of thecolor component to the average of neighboring color components in thesame color plane.
 44. A method as recited in claim 39, wherein each ofsaid at least one first grouping is positioned so as not to overlap anyother of said at least one first grouping.
 45. A method as recited inclaim 39, wherein each said comparison elements has a particularposition in said comparison array, said method further comprising:determining an average percentage of said affirmative andnon-affirmative likeness of each element of said comparison elementshaving a same particular position in all arrays of said at least onecomparison array, and forming a detection array of elements havingone-to-one element correspondence with said comparison elements, whereineach element of said detection array of elements contains said averagepercentage.
 46. A method as recited in claim 45, further comprising thesteps of: providing a visualizer pattern of pixels represented by anarray having visualizer pixels which have one-to-one elementcorrespondence with said detection array, each of said visualizer pixelshas a first logical value if a corresponding visualizer pixel is black,and a complementary logical value if said corresponding pixel is white;forming a visualizer coincidence image having a plurality of coincidencepixels, wherein a coincidence pixel has a corresponding visualizer pixeland a corresponding detection array element; and setting saidcoincidence pixel to black if both said corresponding visualizer pixelis black and said percentage average of said corresponding detectionarray element has a value greater than a predetermined detectionthreshold, otherwise setting said coincidence pixel to white.
 47. Amethod as recited in claim 39, wherein said image has three colorplanes.
 48. An article of manufacture comprising a computer usablemedium having computer readable program code means embodied therein forcausing detection of a watermark in a marked image, the computerreadable program code means in said article of manufacture comprisingcomputer readable program code means for causing a computer to effectthe steps of claim
 39. 49. A method as recited in claim 39, wherein theimage is a marked image, and the step of providing includes alteringsaid marked image employing a blurring filter.
 50. An apparatus fordetecting a watermark comprising mechanisms for implementing the methodof claim
 39. 51. A method comprising generating a visual representationof a data array of data elements having a data array size, including thesteps of: providing a visualizer pattern of visualizer pixelsrepresented by a visualizer array of visualizer pixels, said visualizerarray having a visualizer array size equal to said data array size;forming a visualizer-coincidence image of image pixels represented by animage array having an image array size equal to said visualizer arraysize; setting each said visualizer-coincidence pixel to the color ofsaid corresponding visualizer pixel if a value of said correspondingdata element is above a predetermined threshold and to another color ifsaid value is below said predetermined threshold; and displaying saidvisualizer-coincidence image to form said visual representation.
 52. Amethod as recited in claim 51, wherein said data array represents dataresulting from a watermark detection implementation.
 53. An article ofmanufacture comprising a computer usable medium having computer readableprogram code means embodied therein for causing generation of a visualrepresentation of a data array of data elements, the computer readableprogram code means in said article of manufacture comprising computerreadable program code means for causing a computer to effect the stepsof claim
 52. 54. A method as recited in claim 51, wherein said firstcolor is black and said second color is white.
 55. A method as recitedin claim 51, wherein said threshold is set at a fifty percent successrate.
 56. An article of manufacture comprising a computer usable mediumhaving computer readable program code means embodied therein for causinggeneration of a visual representation of a data array of data elements,the computer readable program code means in said article of manufacturecomprising computer readable program code means for causing a computerto effect the steps of claim
 51. 57. A method for demonstrating anexistence of a watermark in a marked image, said image having aplurality of image pixels, said method comprising: providing avisualizer pattern represented by an array of visualizer elements, eachof said visualizer elements corresponding with one pixel of a pluralityof visualizer pixels and having a first value if said one pixel has afirst color and a second value if said one pixel has a second color,said visualizer array having a visualizer array size; implementing awatermark detection scheme and computing a coincidence value for each ofsaid image pixels within a plurality of pixel selector arrays taken fromamong said image pixels, each of said pixel selector arrays having aselector array size equal to said visualizer array size; forming adetection array from a plurality of coincidence values, wherein saiddetection array has a detection array size equal to said visualizersize; and computing a coincidence detection value for each of saidvisualizer elements such that said detection value represents avisualizer.
 58. An article of manufacture comprising a computer usablemedium having computer readable program code means embodied therein forcausing demonstration of an existence of a watermark in a marked image,the computer readable program code means in said article of manufacturecomprising computer readable program code means for causing a computerto effect the steps of claim
 57. 59. An apparatus for demonstrating anexistence of a watermark in a marked image comprising mechanisms forimplementing the method of claim
 57. 60. A method for detecting awatermark in a marked image having a plurality of image pixels, saidmarked image marked by a watermarking plane having a plurality ofwatermarking elements, said method comprising: providing a visualizerpattern having a plurality of visualizer pixels and a visualizer size;aligning said watermarking plane with said marked image such that eachsaid image pixel has a corresponding watermarking element; generating astatistically related variable for each image element in a plurality ofgroupings of image elements in relationship with said correspondingwatermarking element; wherein each of said groupings has a grouping sizeequal to said visualizer size; averaging said variable for each elementin a like position of all of said groupings to obtain a compositedetection success value; and displaying detection success values by aplurality of visualizer-coincidence pixels having a size equal to saidvisualizer size, each said visualizer-coincidence pixel having a samecolor as said corresponding visualizer pixel when said correspondingsuccess value indicates detection success and another color otherwise.61. A computer program product comprising a computer usable mediumhaving computer readable program code means embodied therein for causingdetection of a watermark in a marked image, the computer readableprogram code means in said computer program product comprising computerreadable program code means for causing a computer to effect the stepsof claim
 60. 62. An article of manufacture as recited in claim 61,wherein the image is a marked image, and the step of aligning includesaltering said marked image employing a blurring filter.
 63. A method asrecited in claim 60, wherein the image is a marked image, and the stepof aligning includes altering said marked image employing a blurringfilter.
 64. An apparatus for detecting a watermark comprising mechanismsfor implementing the method of claim
 60. 65. A computer program productcomprising a computer usable medium having computer readable programcode means embodied therein for causing a watermark to be imparted intoan image, the computer readable program code means in said computerprogram product comprising computer readable program code means forcausing a computer to effect the steps of: providing a digitized imagehaving at least one image plane, said image plane being represented byan image array having a plurality of pixels, each of said pixels havingat least one color component, said watermark being formed using adistinct watermarking plane represented by an array having a pluralityof distinct watermarking elements, each of said distinct watermarkingelements having an array position and having one-to-one positionalcorrespondence wit said image pixels, and multiplying brightness dataassociated with said at least one color component by a predeterminedbrightness multiplying factor, wherein said brightness multiplyingfactor is a corresponding distinct watermarking element, and saidwatermark has a invisibility classification, wherein said distinctwatermarking element, has a value being in the domain greater than orequal to zero and less than or equal to one.
 66. A method of generatinga visual representation of a data array of data elements having a dataarray size, said method comprising: providing a visualizer pattern ofvisualizer pixels represented by a visualizer array of visualizerelements, said visualizer array having a visualizer array size equal tosaid data array size, wherein each of said visualizer elements has afirst logical value if a corresponding visualizer pixel is a first colorand a complementary logical value if said corresponding visualizer pixelhas a second color; forming a data image of image pixels represented byan image array having an image array size equal to said data array size,wherein an image pixel has a corresponding data element and acorresponding visualizer pixel; setting said data pixel to a color ofsaid corresponding visualizer pixel if a value of said data element isabove a predetermined threshold and to another color if said value isbelow said predetermined threshold; and displaying said data image toform said visual representation.
 67. A method as recited in claim 66,wherein said data array represents data resulting from a watermarkdetection implementation.
 68. A method as recited in claim 66, whereinsaid first color is black and said second color is white.
 69. A methodas recited in claim 66, wherein said threshold is set at a fifty percentsuccess rate.
 70. An article of manufacture comprising a computer usablemedium having computer readable program code means embodied therein forcausing generation of a visual representation of a data array of dataelements, the computer readable program code means in said article ofmanufacture comprising computer readable program code means for causinga computer to effect the steps of claim
 66. 71. A computer programproduct comprising a computer usable medium having computer readableprogram code means embodied therein for causing generation of a visualrepresentation of a data array of data elements, the computer readableprogram code means in said computer program product comprising computerreadable program code means for causing a computer to effect the stepsof claim
 66. 72. A method for detecting a watermarking plane comprisingthe steps of: providing an image having a plurality of image pixels,u(i,j), with said image having I rows and J columns, and a pixel in rowi and column j having at least one component, marked by a watermarkingplane; said watermarking plane having a plurality of watermarkingelements, w(i,j), with said watermarking plane having I rows and Jcolumns, and an element in row i and column j having a brightnessmultiplying factor; aligning said watermarking plane with said image;identifying a subset of said image elements; and for each pixel, u(i,j),of said subset of image pixels, employing a detection scheme indetermining a probability of watermark detection based on a property ofuniform distribution of the random brightness multiplying factors or therandom brightness adding or subtracting factors.